Alex Ovechkin and Backstrom each had a goal and an assist for the Capitals (34-31-8), who had lost three straight (0-2-1). Dylan Strome had two assists, and Kuemper made 27 saves after missing two games because of an upper-body injury.
Washington pulled within four points of the Pittsburgh Penguins for the second wild card into the Stanley Cup Playoffs from the Eastern Conference with Pittsburgh's 3-2 loss at the Dallas Stars on Thursday.
"I think as a team we played a good game," Carlson said. "It's nice to get some jump, get some real nice plays by everyone tonight. And I think any time you come back, you want to win, that's the most important thing. So yeah, I'm excited."
Nikita Zaitsev scored for the Blackhawks (24-41-6), who have lost three in a row by a combined score of 15-3. Anton Khudobin made 22 saves in his first game since Jan. 15, 2022, with the Dallas Stars following hip surgery last March.
"It's definitely tough right now," Chicago forward Tyler Johnson said. "It's a little embarrassing. We have to play a lot better. We're not sticking to our structure, not sticking to our system and kind of just out there right now, and we've got to compete and play a lot harder for each other."